Books that emphasize Heisenberg picture

In summary, the conversation discusses the recommendation of a textbook that explains the Heisenberg picture in quantum mechanics in a rigorous manner. The recommended book is "Quantum Mechanics - A Modern Development" by Ballentine, where the Heisenberg picture is correctly placed within the development of quantum mechanics. The conversation also mentions the different choices of time evolution in the Heisenberg picture, Schrödinger picture, and Dirac picture. Finally, a good explanation of the Heisenberg picture for relativistic quantum field theory is suggested in Weinberg's "Quantum Theory of Fields, Vol. 1".
  • #1
IvanPavlov
1
0
Hi fellas,

one friends that is Mathematician asked me to recommend some textbook that emphasizes Heisenberg picture and where this picture is rigorously explained. If anyone knows some good book for this I would be grateful :)

Regards,
Ivan
 
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  • #2
Hi Ivan

Trouble is that picture was well and truly superseded when Dirac came up with his transformation theory which generally goes under the name of QM today. It's virtually impossible to rigorously develop QM by the Heisenberg picture alone these days - you can only explain it within the full QM machinery.

I recommend - Ballentine - Quantum Mechanics - A Modern Development:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

Here QM is fairly rigorously developed from just 2 axioms and the Heisenberg picture correctly placed in that development.

Thanks
Bill
 
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  • #3
Any picture is equivalent (in usual QM; there are subtle troubles in QFT, known as Haag's theorem). It's just your choice of how to share the time dependence between the state operator (i.e., the statistical operator) of the system and the (self-adjoint) operators representing observables. This is only defined up to a time-dependent unitary transformation and is known as the choice of the picture. The Heisenberg picture is the one that is most closely related to the way classical mechanics is formulated in terms of the Hamilton formalism using Poisson brackets and lumps all time dependence to the observable operators. The Schrödinger picture is the one where the entire time dependence is put to the statistical operator and the observable operators are time independent. The most general picture is due to Dirac, where you choose one part of the Hamiltonian, [itex]\hat{H}_0[/itex] to propagate the observable operators and one part [itex]\hat{H}_1[/itex] that propagate the statistical operator. In any case you have [itex]\hat{H}_0+\hat{H}_1=\hat{H}[/itex], and the outcome for observable quantities (probability distributions for finding a certain possible value for an observable, average values for observables, transition probabilities like S-matrix elements, etc.) is independent of the choice of the picture of time evolution.

A good explanation of the Heisenberg picture for relativistic QFT is given in

Weinberg, Quantum Theory of Fields, Vol. 1

Usually QFT textbooks use the Heisenberg picture to start with and then derive perturbative QFT (Feynman diagrams) using the interaction picture (usually ignoring Haag's theorem of course ;-)).
 

1. What is the Heisenberg picture in quantum mechanics?

The Heisenberg picture is one of the two commonly used mathematical formulations in quantum mechanics, along with the Schrödinger picture. In this approach, the operators representing physical observables have a time-dependence, while the state vectors remain constant. This allows for a more intuitive understanding of the evolution of quantum systems.

2. How do books emphasizing the Heisenberg picture differ from other quantum mechanics books?

Books that emphasize the Heisenberg picture focus on the mathematical formalism of quantum mechanics, particularly the use of operators and time-dependence. They may also explore the philosophical implications of the Heisenberg uncertainty principle and the role of measurement in quantum systems.

3. What are some examples of books that emphasize the Heisenberg picture?

Some popular books that emphasize the Heisenberg picture include "Quantum Mechanics: The Theoretical Minimum" by Leonard Susskind and Art Friedman, "Quantum Mechanics: A Modern Development" by Leslie E. Ballentine, and "Quantum Mechanics in the Heisenberg Representation" by Werner Heisenberg.

4. Are books that emphasize the Heisenberg picture suitable for beginners in quantum mechanics?

Books that emphasize the Heisenberg picture may be more challenging for beginners in quantum mechanics, as they often assume a basic understanding of the mathematical concepts and principles of quantum mechanics. However, some books may provide a gentle introduction to the Heisenberg picture for beginners.

5. Is the Heisenberg picture still relevant in modern quantum mechanics?

Yes, the Heisenberg picture is still widely used in modern quantum mechanics, particularly in the study of time-dependent systems and in the development of more advanced theories such as quantum field theory. It continues to be a valuable tool for understanding and exploring the behavior of quantum systems.

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